The semiconductor manufacturing process is the era of 45 nm design rule. The production form is shifting from the small item mass production represented by DRAM to the multi item small production like SOC (Silicon on chip). According to this, the number of manufacturing process is increasing, improvement in yield in every process is essential, and an inspection of a defect which is generated in the process become very important.
According to the higher integration of a semiconductor device and the finer patterning, an inspection system of high resolution and high throughput is required. In order to check a defect on a wafer substrate of 45 nm design rule, it is necessary to inspect a pattern defect in the pattern having the line width of 40 nm and less, and further to inspect a defect of a particle. Further, it is necessary to check the electrical defect thereof. According to an increase in the manufacturing process accompanying the higher integration of a device, the amount of inspection is increased. A higher throughput is accordingly required. Further, tendency toward multilayer of a device is accelerated, an inspection system is required to have a function of detecting a contact failure (electrical defect) of a via connecting wire between layers.
Further, the electron gun for an ERL radiation optical source is required a very high brightness and large beam current. (Nishitani et al, Extended Abstracts (The 53rd Spring Meeting, 2006); The Japanese Society of Applied Physics No. 2, p 798). A heavy ion source for a heavy ion radiotherapy is also required a very small Emittance beam.
Seventy four years ago, Langmuir showed that the current density in a focused beam of cathode rays was shown to have an upper limit defined byJ=Jc(eφ/kTc+1)sin2 α,  (1)where J was the maximum current density obtainable in the focused spot, Jc was the current density at the cathode, φ was the voltage at the focus relative to the cathode, e was the electronic charge, k was Boltzmann's constant, α was the half angle subtended by the cone of electrons which converged on the focused spot and Tc was the absolute temperature of the cathode. The necessary initial assumptions were (1) that electrons leaved the cathode with a Maxwellian distribution of velocities, and (2) that the focusing system was free from aberration and obeyed the law of sines.
By using Liouville's theorem instead of the assumption (2), J. R. Pierce defined the same results as the eq. (1). As a result it is seen to be independent of the nature of the concentrating system when only steady fields are involved.
From the equation (1) to obtain the high brightness, the large cathode current density is absolutely necessary, and then a field emission gun and a Schottky cathode electron gun are much used as the high brightness electron gun than the thermal cathode electron gun. As thus the limit has been played a very important part in developments for the high brightness electron gun.